How to get rid of shadowy texture on objects?
It's hard to tell from the images alone what you mean, there may actually be two different issues at play here.

As mentioned by Mr Zak you could easily make your arrows shadeless either by


Increasing Emission -  This will make the object as if it were emitting light, it will partly retain shadows and glossy reflections (with the right render settings you can even actually maker them glow if you render with Blender Internal)
Turning on the option Shadeless under the Properties Window > Material Options > Shading - This Will make your object flat colored, as if it were bi-dimensional, no shadows, no glossiness, or shine, and no light emission (basically doesn't react to lighting)


There is another issue at play here, that may be slightly messed up normals which will yield weird or unexpected shading. Use an edge split modifier on all your objects to make shading as expected.

Have in mind that switching to Blender Cycles may not be a full lasting solution on it's own, it will require setting up materials and scene differently from scratch since they are two completely separate and independent render engines, and Blender Internal materials are incompatible with Cycles and vice-versa